Now the next task is to make sure the floor you are working on is
solid and stable. I started with the plywood from the original
construction in perfect shape, no water damage and the nails tight. If
that isn't the case for your job, you will need to repair or replace
that first. Make sure you do it right, because you want the tile floor
to last and not move or break!

Next, you need to apply the subfloor that will be stable for tile. I
used 1/4" cement board designed for this purpose.

You will want to cut and break this stuff like sheetrock. Use a sharp
utility knife with a straight edge and I would make a couple of passes
to get deep enough to allow it to break fairly clean. You then screw
down the sheets with 1" to 1-1/2" screws depending on your floor. Make
sure the screw heads are sunk in a bit to keep from putting pressure on
tiles later. Make sure you use the right kind of screws, so ask
questions when buying them.